Model network of a nonlinear circuitry

ABSTRACT

A model network of a nonlinear circuitry includes one or more static nonlinear elements and a plurality of linear filters with transfer functions. A method for determining the model network includes performing an input amplitude-to-output amplitude measurement of the nonlinear circuitry and performing an input amplitude-to-output phase measurement of the nonlinear circuitry. The transfer functions are calculated on the basis of results of the input amplitude-to-output amplitude measurement and input amplitude-to-output phase measurement.

FIELD OF THE INVENTION

The invention relates to nonlinear systems and more specifically tomodeling and predistortion linearization of nonlinear circuitry forcommunications systems.

BACKGROUND OF THE INVENTION

In many technical fields, linearization of nonlinear circuitry is usedto compensate for unwanted effects caused by the nonlinear behavior ofthe nonlinear circuitry. One possibility to linearize nonlinearcircuitry is to predistort the signal input into the nonlinear circuitryto ensure that the output signal of the nonlinear circuitry is, in theideal case, linearly related to the input signal of the predistorter.

Power amplifiers are used in wireline and wireless communicationssystems for transferring high-rate data signals from a transmitter to areceiver. Power amplifiers are highly cost intensive during productionand also during operation. Therefore, it is desirable to operate poweramplifiers in a most efficient way. As the efficiency of a poweramplifier increases with nonlinearity, power amplifiers are typicallydriven in the nonlinear region. This leads to spectral regrowth andintermodulation distortion in the amplified signal band. These effectsincrease the bit error rate at the receiver and cause unacceptably highco-channel interference.

As a countermeasure to decrease the unwanted effects of nonlinearity, apredistorter may be employed to predistort the signal input to the poweramplifier. Signal predistortion allows creation of low-price transmitterdevices fulfilling given spectral masks for the transmission signal eventhough the power amplifier is driven in the nonlinear region.

It is known to use models (i.e. model networks) to approximatelyreproduce the nonlinear behavior of the power amplifier or, generallyspeaking, the nonlinear circuitry. These models may be used forsimulation purposes, for instance to perform a bit error ratesimulation. They may also be used for the purpose of minimizing theunwanted effects caused by the nonlinear behavior of the nonlinearcircuitry.

Typically, nonlinear circuitry is modeled by a network comprising twostatic nonlinearities called amplitude-to-amplitude modulationconversion (AM/AM-conversion) and amplitude-to-phase modulationconversion (AM/PM-conversion). The AM/AM-conversion maps an input signalamplitude into an output signal amplitude, which may, for instance, berepresented by a series expansion around the input signal amplitude.Analogously, the AM/PM-conversion maps an input signal amplitude into anoutput signal phase, which may equally be represented by a seriesexpansion around the input signal amplitude. Generally, both staticnonlinearities are purely dependent on the input signal magnitude.Identifying the nonlinear circuitry means to determine these two staticnonlinearities—i.e. the coefficients of the series expansions in casethe nonlinearities are expressed by series. Conventionally, this may beaccomplished by simple two-tone or single-tone measurements. In thesemeasurements, the power of the input signal to the nonlinear circuitryis varied and the power and the phase difference of the fundamentals atthe output of the nonlinear circuitry are recorded.

Dynamic effects, also known as memory effects, are another problemencountered in nonlinear circuitries. Memory effects in power amplifierstypically show up as a non-symmetrical spectrum around the carrier atthe output of the power amplifier. They are caused by thermal orelectro-thermal processes in the power amplifier. As the term “memoryeffects” indicates, there is a dependency not only on the present value,e.g. sample, but also on previous values, e.g. samples, of the inputsignal.

Conventional concepts based on static AM/AM-conversion andAM/PM-conversion cannot model the dynamic or memory behavior of thepower amplifier. However, the compensation of memory effects isespecially important for radio frequency wideband applications.

From a theoretical point of view, it is possible to model such dynamicor memory effects by identifying the nonlinear circuitry by means ofadaptive algorithms, for instance LMS (least means squares), RLS(recursive least squares). However, this requires in general a costlymeasurement system comprising a complex signal generator,analog-to-digital converters, a digital signal processor etc. Comparedto the AM/AM and AM/PM measurements, which may be carried out by asimple network analyzer using a one-tone or two-tone input signalaccording to the conventional approach. The use of adaptive algorithmsinvolves significantly higher computational efforts and systemrequirements.

SUMMARY OF THE INVENTION

The following presents a simplified summary in order to provide a basicunderstanding of one or more aspects and/or embodiments of theinvention. This summary is not an extensive overview of the invention,and is neither intended to identify key or critical elements of theinvention, nor to delineate the scope thereof. Rather, the primarypurpose of the summary is to present one or more concepts of theinvention in a simplified form as a prelude to the more detaileddescription that is presented later.

A model network of a nonlinear circuitry comprises one or more staticnonlinear elements and a plurality of linear filters with transferfunctions. A method for determining the model network comprisesperforming an input amplitude-to-output amplitude measurement of thenonlinear circuitry and performing an input amplitude-to-output phasemeasurement of the nonlinear circuitry. The transfer functions arecalculated on the basis of results of the input amplitude-to-outputamplitude measurement and input amplitude-to-output phase measurement.

To the accomplishment of the foregoing and related ends, the inventioncomprises the features hereinafter fully described and particularlypointed out in the claims. The following description and the annexeddrawings set forth in detail certain illustrative aspects andimplementations of the invention. These are indicative, however, of buta few of the various ways in which the principles of the invention maybe employed. Other objects, advantages and novel features of theinvention will become apparent from the following detailed descriptionof the invention when considered in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the invention are made more evident in the following detaileddescription of some embodiments when read in conjunction with theattached drawing figures, wherein:

FIG. 1 is a model network constructed with memory polynomials fordescribing the nonlinear behavior of a power amplifier;

FIG. 2 is a diagram illustrating a two-dimensional time-domain Volterrakernel and the corresponding diagonal kernel.

FIG. 3 is a block diagram illustrating a system for performing frequencydependent AM/AM and AM/PM measurements;

FIG. 4 is a diagram illustrating the amplifier output power versus atwo-dimensional amplifier input power and amplifier input frequencyrepresentation; and

FIG. 5 is a diagram illustrating the amplifier output power versus atwo-dimensional amplifier input power and amplifier input frequencyrepresentation.

DETAILED DESCRIPTION OF THE INVENTION

From nonlinear system theory it is known that a nonlinear system orcircuit may be described in terms of Volterra kernels. Briefly, thenonlinear system may be represented by an operator H. It is assumed thatan input signal

x(t)=a(t)·cos(ω_(c) t+φ(t)  (1)

is input into the nonlinear system, with ω_(c) being the carrierfrequency, φ(t) being the time-dependent phase and a(t) being thetime-dependent amplitude of the input signal. The output signal of thenonlinear system may be expressed by

$\begin{matrix}{{{y(t)} = {{H\lbrack {x(t)} \rbrack} = {\sum\limits_{n = 1}^{N}\; {y_{n}(t)}}}}{y_{n}(t)} = {\int_{0}^{\infty}{\cdots {\int_{0}^{\propto}{{h_{n}( {\tau_{1},\ldots \mspace{11mu},\tau_{n}} )}{\prod\limits_{i = 1}^{n}\; {{x( {t - \tau_{i}} )}\ {{{t\ }_{i}}.}}}}}}}} & (2)\end{matrix}$

Thus, the output signal y(t) is expanded in a series of componentfunctions y_(n)(t). Each component function y_(n)(t) is described by aVolterra integral, wherein the number N of component functions denotesthe order of the nonlinearity. The terms h_(n)(τ₁, . . . , τ_(n)) areknown as (time-domain) Volterra kernels of the order n.

From equation (2), it is apparent that Volterra kernels h_(n)(τ₁, . . .τ_(n)) are used to describe a nonlinear system in a similar way as theimpulse response is used to describe a linear system. In linear systemtheory, the output signal of a linear system is the convolution of theinput signal with the impulse response. Analogously, the output signaly(t) of the nonlinear system is the multi-dimensional convolution of theinput signal x(t) with a series expansion of Volterra kernels h_(n)(τ₁,. . . , τ_(n)). In fact, the first order Volterra kernel h₁(τ) isidentical to the impulse response of a linear system. As the concept ofdescribing a system by an impulse response is limited to linear systems,the Volterra kernel representation may be intuitively understood as ageneralization of the impulse response concept to nonlinear systems.

Memory polynomials are a simplified complex baseband Volterra model inwhich only Volterra kernels along the diagonals in the multi-dimensionalspace and not the full Volterra kernels are considered, i.e.

{tilde over (h)}_(2k+1)(τ₁, . . . , τ_(2k+1))≡0 for τ₁≠τ₂≠ . . .≠τ_(2k+1).  (3)

It is to be noted that even order kernels do not exist in the basebandVolterra representation, and therefore, the index n is replaced by 2k+1.“{tilde over ( )}” is used to indicate that the symbol beneath refers toa baseband quantity.

Thus, the continuous-time memory polynomial model can be expressed by

$\quad\begin{matrix}\begin{matrix}{{\overset{\sim}{y}(t)} = {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}\; {\int_{0}^{\infty}{{{\overset{\sim}{g}}_{{2k} + 1}(\tau)}{{\overset{\sim}{x}( {t - \tau} )}}^{2k}{\overset{\sim}{x}( {t - \tau} )}\ {\tau}}}}} \\{= {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{{{\overset{\sim}{g}}_{{2k} + 1}(t)}*{{\overset{\sim}{x}(t)}}^{2k}{\overset{\sim}{x}(t)}}}}\end{matrix} & (4)\end{matrix}$

where {tilde over (g)}_(2k+1)(τ)≡{tilde over (h)}_(2k+1)(τ, . . . , τ)describes the time-domain Volterra kernels along the diagonals in amulti-dimensional space, and “*” denotes the convolution operator. Lcorresponds to N in equation (2), i.e. denotes the order of thenonlinearity.

FIG. 1 illustrates a complex baseband model constructed with memorypolynomials. The model comprises a bank of static nonlinearities 1, 2given by |{tilde over (x)}|²{tilde over (x)}, |{tilde over (x)}|⁴{tildeover (x)}, . . . , |{tilde over (x)}|^(2k){tilde over (x)} and unknownlinear filters 3, 4, 5. The static nonlinearities 1, 2 are arranged inparallel and are each serially coupled to one of the unknown linearfilters 4, 5. The baseband input signal {tilde over (x)}(t) is fed intothe input of linear filter 3. The outputs of the filters 3, 4, 5 arecombined by an adder 6 to yield the output signal {tilde over (y)}(t).{tilde over (G)}_(2k+1)(ω_(m))=F{{tilde over (g)}_(2k+1)(t)} denotes theFourier transform of the diagonal time-domain Volterra kernels in (4)for k=0, . . . , K where K=┌L/2┐−1.

FIG. 2 illustrates a two-dimensional baseband time-domain Volterrakernel {tilde over (h)}₂(τ₁, τ₂), the cut along the diagonal τ₁=τ₂ andthe corresponding diagonal baseband time-domain Volterra kernel {tildeover (g)}₂(τ)≡{tilde over (h)}₂(τ, τ). As even-order kernels do notexist in the baseband Volterra representation, FIG. 2 serves simply toshow the concept of diagonal kernels.

Embodiments of the invention contemplate that the two-tone response of acomplex Volterra system can be expressed in a similar form as thetwo-tone response of a quasi-memoryless system. This makes it possibleto identify a memory-containing nonlinear circuitry represented by themodel network depicted in FIG. 1 by performing simple two-tonemeasurements of the nonlinear circuitry (e.g. power amplifier). Thesemeasurements, which will be explained below in conjunction with FIG. 3,only require standard measurement equipment, namely a sinewave generatorand a network analyzer.

FIG. 3 is a block diagram of an exemplary measurement setup. A signalsource, i.e. sinewave generator 10 generates a two-tone RF (radiofrequency) signal x(t)=a[cos((ω_(c)+ω_(m))t)+cos((ω_(c)−ω_(m))t)] to beinput into a power amplifier (PA) 11. ω_(m) is a tuning frequency. Thepower amplifier 11 may be for instance a 2.2-GHz, 90-W Class AB RF poweramplifier. The power amplifier 11 output y(t) is coupled to an input ofa bandpass filter (BPF) 12 having its center frequency at±(ω_(c)+ω_(m)). The filtered signal y_(f)(t), i.e. the fundamental ofthe output signal spectrum at ω_(m), is examined in a signal analyzer,i.e. network analyzer 13 in view of its amplitude a and the relativephase of the filtered signal y_(f)(t) in relation to the signal phase atthe input of the power amplifier 11.

In the following, calculation of the transfer functions {tilde over(G)}_(2k+1)(ω) of the unknown linear filters 3, 4, 5 of the complexbaseband model depicted in FIG. 1 for k=0, . . . , K is shown. Thebaseband two-tone signal corresponding to the passband signal x(t) isdenoted by {tilde over (x)}(t)=a cos(ω_(m)t+φ). If this basebandtwo-tone signal {tilde over (x)}(t) is applied to the memory polynomialmodel of equation (4), it is obtained

$\begin{matrix}{{\overset{\sim}{y}(t)} = {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{( \frac{a}{2} )^{{2k} + 1}{\int_{0}^{\infty}{{{{\overset{\sim}{g}}_{{2k} + 1}(\tau)}\lbrack {{\exp ( {j( {{\omega_{m}( {t - \tau} )} + \varphi} )} )} + {\exp ( {- {j( {{\omega_{m}( {t - \tau} )} + \varphi} )}} )}} \rbrack}^{{2k} + 1}\ {{t}.}}}}}} & (5)\end{matrix}$

By evaluating the (2k+1)-th power of the expression within the bracketsof equation (5), equation (5) can be rewritten as

$\begin{matrix}{{\overset{\sim}{y}(t)} = {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{( \frac{a}{2} )^{{2k} + 1}{\sum\limits_{n = 0}^{{2k} + 1}\; {\begin{pmatrix}{{2k} + 1} \\n\end{pmatrix}{\exp \lbrack {j( {{( {{2n} - {2k} - 1} )\omega_{m}t} + {( {{2n} - {2k} - 1} )\varphi}} )} \rbrack} \times {\int_{0}^{\infty}{{{\overset{\sim}{g}}_{{2k} + 1}(\tau)}{\exp ( {{- {j( {{2n} - {2k} - 1} )}}\omega_{m}\tau} )}\ {{\tau}.}}}}}}}} & (6)\end{matrix}$

This yields for the fundamental angular frequency at ω_(m) with n=k+1

$\begin{matrix}{{{\overset{\sim}{y}}_{f}(t)} = {{\exp ( {j( {{\omega_{m}t} + \varphi} )} )}{\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{( \frac{a}{2} )^{{2k} + 1}\begin{pmatrix}{{2k} + 1} \\{k + 1}\end{pmatrix}{{{\overset{\sim}{G}}_{{2k} + 1}( \omega_{m} )}.}}}}} & (7)\end{matrix}$

This equation contains the unknown linear filters {tilde over(G)}_(2k+1)(ω) for k=0, . . . , K.

Thus, the filtered two-tone response of the baseband complex memorypolynomial model in equation (7) can be rewritten as

$\begin{matrix}{{{{\overset{\sim}{y}}_{f}(t)} = {{{v( {a,\omega_{m}} )}}{\exp ( {j( {{\omega_{m}t} + \varphi + {\arg \{ {v( {a,\omega_{m}} )} \}}} )} )}}}{where}} & (8) \\{{v( {a,\omega_{m}} )} = {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{( \frac{a}{2} )^{{2k} + 1}\begin{pmatrix}{{2k} + 1} \\{k + 1}\end{pmatrix}{{{\overset{\sim}{G}}_{{2k} + 1}( \omega_{m} )}.}}}} & (9)\end{matrix}$

It is apparent that the two-tone response of the complex basebandVolterra system in equation (8) is in a similar form as the response ofa quasi-memoryless system. For this reason |v(a,ω)| in equation (8) isdefined as the frequency-dependent AM/AM-conversion and arg{v(a,ω)} inequation (8) as the frequency-dependent AM/PM-conversion.

v(a,ω_(m)) describes a complex function which depends on both, thesignal amplitude a and the modulation frequency ω_(m) of the inputsignal. Because the memory polynomial model in equation (4) is purelydependent on the ┌L/2┐ complex linear filters (diagonal frequency-domainVolterra kernels), it is possible to estimate them from the measuredfrequency-dependent AM/AM-conversion and AM/PM-conversion in equation(9) for ┌L/2┐ different input signal magnitudes a_(i), i=1, . . . ,┌L/2┐.

In one embodiment of the invention, the network analyzer may comprise ameasurement unit and a calculation unit such as a processor orcontroller unit. Alternately, a separate processor or controller may beemployed to perform the above calculations and any such embodiments arecontemplated as falling within the scope of the invention.

FIG. 4 shows the output power P_(O)=10 log(|v(a,ω)|²/(2R×10⁻³)) of thesimulated frequency-dependent AM/AM-conversion of the 2.2-GHz, 90-WClass AB RF power amplifier 11 excited with the passband two-tone signalx(t) over the input signal power range of P_(I)=10log(a²/(2R×10⁻³))=(−10 . . . 42) dBm, where R=50Ω denotes the inputimpedance of the RF power amplifier 11. The modulation frequency rangesfrom ω_(m)/(2π)=(6 . . . 60) MHz. The corresponding frequency-dependentAM/PM-conversion is depicted in FIG. 5 and yields arg{v(a,ω_(m))}.

Taking into account equation (9), it is sufficient to measure thetwo-dimensional areas depicted in FIGS. 4 and 5 to calculate the unknowncomplex linear filters 3, 4, 5 in the complex baseband model constructedwith memory polynomials (FIG. 1).

Because in practical applications, these measurements are noisy(imperfect measurements, model inaccuracies), a classical linear leastsquares problem may be formulated to estimate the unknown linear filters{tilde over (G)}_(2k+1)(ω_(m)) in equation (9) by

Ĝ(ω_(m))=(A ^(T) A)⁻¹A^(T) {circumflex over (v)}(ω_(m))  (10)

where

{circumflex over (v)}(ω_(m))=[{circumflex over (v)}(a₁,ω_(m)),{circumflex over (v)}(a ₂,ω_(m)), . . . , {circumflex over(v)}(a _(N),ω_(m))]^(T)  (11)

denotes an N×1 vector (N>┌L/2┐), whose components are the measured(noisy) versions of the frequency-dependent AM/AM and AM/PM-conversionentries in equation (9). The ┌L/2×┐1 vector

Ĝ(ω_(m))=[Ĝ ₁(ω_(m)),Ĝ ₃(ω_(m)), . . . , Ĝ _(2┌L/2┐−1)(ω_(m))]^(T)  (12)

describes the estimated linear filters 3, 4, 5 in FIG. 1 for themodulation frequency ω_(m).

The N×┌L/2┐ observation matrix A in equation (10) is defined by

$\begin{matrix}{A = {\begin{pmatrix}\frac{a_{1}}{2} & {3( \frac{a_{1}}{2} )^{3}} & \cdots & \begin{pmatrix}{{2\lceil \frac{L}{2} \rceil} - 1} \\\lceil \frac{L}{2} \rceil\end{pmatrix} & ( \frac{a_{1}}{2} )^{{2{\lceil\frac{L}{2}\rceil}} - 1} \\\vdots & \vdots & \; & \vdots & \; \\\frac{a_{N}}{2} & {3( \frac{a_{N}}{2} )^{3}} & \cdots & \begin{pmatrix}{{2\lceil \frac{L}{2} \rceil} - 1} \\\lceil \frac{L}{2} \rceil\end{pmatrix} & ( \frac{a_{N}}{2} )^{{2{\lceil\frac{L}{2}\rceil}} - 1}\end{pmatrix}.}} & (13)\end{matrix}$

To obtain the frequency responses of the unknown linear filters {tildeover (G)}_(2k+1)(ω) over the frequency-range of interest, the leastsquares problem in equation (10) is solved for different modulationfrequencies ω_(m). The number of parameters required to model the poweramplifier 11 in the baseband-domain by the memory polynomial modeldepicted in FIG. 1 is dependent from the design of the linear filters 3,4, 5 and K. As already mentioned, K is related to the order of thenonlinearity of the power amplifier 11 and can be estimated from thefrequency-dependent AM/AM-conversion and AM/PM-conversion measurements.

Further, it is to be noted that the frequency-dependent AM/AM-conversionand AM/PM-conversion can not only be considered for the fundamental ofthe output signal spectrum at ω_(m). It can also be derived for theharmonics of the input signal, e.g. the third-order intermodulationdistortion (IMD3) at 3ω_(m). In this case, the bandpass filter 12 shouldhave a center frequency at ±(ω_(c)+3ω_(m)).

The above scheme for constructing memory polynomial models fromfrequency-dependent AM/AM-measurements and AM/PM-measurements may begeneralized to any complex Volterra model in which only thefrequency-domain Volterra kernels along the diagonals are considered.Thus, although the concept outlined above does not fully describe anyVolterra system (because Volterra kernels outside the diagonals arediscarded), the concept, on the other hand, is not limited to memorypolynomials. If the concept of the AM/AM-conversion and theAM/PM-conversion is extended for more general nonlinear models as memorypolynomial models, the baseband two-tone response of the power amplifier11 may be written as

$\begin{matrix}{{\overset{\sim}{y}(t)} = {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{( \frac{a}{2} )^{{2k} + 1}{\sum\limits_{n_{1} = 1}^{2}{\cdots {\sum\limits_{n_{{2k} + 1} = 1}^{2}{{\exp ( {j{\sum\limits_{i = 1}^{{2k} + 1}{( {- 1} )^{n_{i} + 1}\omega_{m}t}}} )} \times {{{\overset{\sim}{H}}_{{2k} + 1}( {{( {- 1} )^{n_{1} - 1}\omega_{m}},\ldots \mspace{11mu},{( {- 1} )^{n_{{2k} + 1} - 1}\omega_{m}}} )}.}}}}}}}} & (14)\end{matrix}$

{tilde over (H)}_(2k+1)(ω₁, . . . ω_(k+1)) are the frequency-domainbaseband Volterra kernels associated to the time-domain Volterra kernels{tilde over (h)}_(2k+1)(τ₁, . . . , τ_(2k+1)) set out in equation (3).If this two-tone response is passed through the complex linear filter 12(center angular frequency is ω_(m)) and the magnitude a and the angularfrequency ω_(m) of the input signal is swept, one obtains

$\begin{matrix}{{{{\overset{\sim}{y}}_{f}(t)} = {{\exp ( {j( {{\omega_{m}t} + \varphi} )} )}{\sum\limits_{k = 0}^{\lceil{L/2}\rceil}{( \frac{a}{2} )^{{2k} + 1}\begin{pmatrix}{{2k} + 1} \\{k + 1}\end{pmatrix} \times {\overset{\sim}{H}}_{{2k} + 1}\underset{{({k + 1})} \times}{\underset{}{( {\omega_{m},\ldots \mspace{11mu},\omega_{m}} }}}}}},{\underset{k \times}{\underset{}{ {{- \omega_{m}},\ldots \mspace{11mu},{- \omega_{m}}} )}}.}} & (15)\end{matrix}$

Here, it is assumed without loss of generality that the Volterra kernelsare symmetric. The two-tone response of the complex Volterra model inequation (15) can also be rewritten in the following form

$\begin{matrix}{{{{\overset{\sim}{y}}_{f}(t)} = {{{v( {a,\omega_{m}} )}}{\exp ( {j( {{\omega_{m}t} + \varphi + {\arg \{ {v( {a,\omega_{m}} )} \}}} )} )}}}{where}} & (16) \\{{{v( {a,\omega_{m}} )} = {\sum\limits_{k = 0}^{{\lceil{L/2}\rceil} - 1}{( \frac{a}{2} )^{{2k} + 1}\begin{pmatrix}{{2k} + 1} \\{k + 1}\end{pmatrix}{\overset{\sim}{H}}_{{2k} + 1}\underset{{({k + 1})} \times}{\underset{}{( {\omega_{m},\ldots \mspace{11mu},\omega_{m}} }}}}},\underset{k \times}{\underset{}{ {{- \omega_{m}},\ldots \mspace{11mu},{- \omega_{m}}} )}}} & (17)\end{matrix}$

describes a complex function which depends on both, the signal amplitudea and the modulation frequency ω_(m) of the input signal. Again, asalready explained in conjunction with equation (8), equation (16) is ina similar form as the response of a quasi-memoryless system resulting inthat {tilde over (H)}_(2k+1)(ω₁, . . . , ω_(2k+1)) can be calculated onthe basis of a simple one or two-tone measurement by sweeping thefrequency and amplitude of the RF input signal.

The method for determining the transfer functions of linear filters in amodel network of a nonlinear circuitry by two-tone AM/AM and AM/PMmeasurements can be analogously be applied for calculation of filtertransfer functions of a predistorter preceding an amplifier. Thepredistorter has a design corresponding to the memory polynomial designof the amplifier model depicted in FIG. 1, i.e. includes staticnonlinearities and linear filters. The predistorter filter transferfunctions can be derived from the filter transfer functions calculatedfor the amplifier model as outlined above.

Therefore the present invention contemplates a method of configuring apredistorter unit in conjunction with the use of nonlinear circuitrysuch as a power amplifier operated in a nonlinear range in order tooperate at high efficiency. Such configuration then includes performingamplitude-amplitude and amplitude phase measurements and calculating thetransfer functions for the nonlinear circuitry and using such results toconfigure the predistorter. In the above fashion, the output of thenonlinear circuitry is substantially linear with respect to the input ofthe predistorter, thereby reducing distortion and advantageouslydecreasing the bit error rate in communication systems.

While the invention has been illustrated and described with respect toone or more implementations, alterations and/or modifications may bemade to the illustrated examples without departing from the spirit andscope of the appended claims. In particular regard to the variousfunctions performed by the above described components or structures(assemblies, arrangement, devices, circuits, systems, etc.), the terms(including a reference to a “means”) used to describe such componentsare intended to correspond, unless otherwise indicated, to any componentor structure which performs the specified function of the describedcomponent (e.g., that is functionally equivalent), even though notstructurally equivalent to the disclosed structure which performs thefunction in the herein illustrated exemplary implementations of theinvention. In addition, while a particular feature of the invention mayhave been disclosed with respect to only one of several implementations,such feature may be combined with one or more other features of theother implementations as may be desired and advantageous for any givenor particular application. Furthermore, to the extent that the terms“including”, “includes”, “having”, “has”, “with”, or variants thereofare used in either the detailed description and the claims, such termsare intended to be inclusive in a manner similar to the term“comprising”.

1. A method for determining a model network of nonlinear circuitryhaving an input and an output, the model network comprising one or morestatic nonlinear elements and a plurality of linear filters withtransfer functions, comprising: performing an input amplitude-to-outputamplitude measurement of the nonlinear circuitry, performing an inputamplitude-to-output phase measurement of the nonlinear circuitry, andcalculating the transfer functions of the linear filters on the basis ofresults of the input amplitude-to-output amplitude measurement and inputamplitude-to-output phase measurement.
 2. The method of claim 1, whereinthe input amplitude-to-output phase (AM/PM) measurement comprises:coupling a test signal into the input of the nonlinear circuitry;sweeping a frequency and an amplitude of the test signal; and measuringa phase of a signal at the output of the nonlinear circuitry over theswept frequency and swept amplitude test signal.
 3. The method of claim2, wherein the test signal comprises two tones of different frequencies,and the frequency for sweeping is the difference between the differentfrequencies of the two tones.
 4. The method of claim 3, wherein the testsignal has exactly two tones of different frequencies.
 5. The method ofclaim 1, wherein the input amplitude-to-output amplitude measurementcomprises: coupling a test signal into the input of the nonlinearcircuitry; sweeping a frequency and an amplitude of the test signal; andmeasuring an amplitude of a signal at the output of the nonlinearcircuitry over the swept frequency and swept amplitude test signal. 6.The method of claim 1, further comprising using a two-tone networkanalyzer for performing the measurements.
 7. The method of claim 1,wherein performing the input amplitude-to-output amplitude measurementand the input amplitude-to-output phase measurement of the nonlinearcircuitry provides a set of measurement result vectors, and whereincomplex value elements of each measurement result vector represent themagnitude and phase of the output signal for different input signalamplitudes at a given input signal frequency.
 8. The method of claim 7,wherein calculating the transfer functions comprises calculatingtransfer function values of the filters on the basis of the set ofmeasurement result vectors.
 9. The method of claim 1, wherein the modelnetwork comprises a baseband model network of the nonlinear circuitryusing memory polynomials.
 10. The method of claim 1, wherein thenonlinear circuitry comprises a power amplifier.
 11. A method forconfiguring a predistorter adapted to linearize nonlinear circuitryhaving an input and an output, the predistorter comprising one or morestatic nonlinear elements and a plurality of linear filters withtransfer functions, comprising: performing an input amplitude-to-outputamplitude measurement of the nonlinear circuitry, performing an inputamplitude-to-output phase measurement of the nonlinear circuitry, andcalculating the transfer functions of the linear filters of thepredistorter on the basis of results of the input amplitude-to-outputamplitude measurement and input amplitude-to-output phase measurement.12. The method of claim 11, wherein the input amplitude-to-output phasemeasurement comprises: coupling a test signal into the input of thenonlinear circuitry; sweeping a frequency and an amplitude of the testsignal; and measuring a phase of a signal at the output of the nonlinearcircuitry over the swept frequency and swept amplitude test signal. 13.The method of claim 12, wherein the test signal comprises two tones ofdifferent frequencies, and the frequency for sweeping is the differencebetween the different frequencies of the two tones.
 14. The method ofclaim 13, wherein the test signal has exactly two tones of differentfrequencies.
 15. The method of claim 11, wherein the inputamplitude-to-output amplitude measurement comprises: coupling a testsignal into the input of the nonlinear circuitry; sweeping a frequencyand an amplitude of the test signal; and measuring an amplitude of asignal at the output of the nonlinear circuitry over the swept frequencyand swept amplitude test signal.
 16. The method of claim 11, furthercomprising using a two-tone network analyzer for performing themeasurements.
 17. The method of claim 11, wherein performing the inputamplitude-to-output amplitude measurement and the inputamplitude-to-output phase measurement of the nonlinear circuitryprovides a set of measurement result vectors, and wherein complex valueelements of each measurement result vector represent the magnitude andphase of the output signal for different input signal amplitudes at agiven input signal frequency.
 18. The method of claim 17, whereincalculating the transfer functions comprises calculating transferfunction values of the filters on the basis of the set of measurementresult vectors.
 19. The method of claim 11, wherein the predistortercomprises a baseband predistorter, and wherein the static nonlinearelements and linear filters thereof are configured to represent memorypolynomials.
 20. A circuit for analyzing nonlinear circuitry having aninput and an output, the nonlinear circuitry being modeled by a modelnetwork comprising one or more static nonlinear elements and a pluralityof linear filters with transfer functions, comprising: a test signalgenerator coupled to the input of the nonlinear circuitry; a measurementunit coupled to the output of the nonlinear circuitry and configured toperform an input amplitude-to-output amplitude measurement and an inputamplitude-to-output phase measurement of the nonlinear circuitry; and acalculation unit operably coupled to the measurement unit and adapted tocalculate the transfer functions on the basis of results of the inputamplitude-to-output amplitude measurement and input amplitude-to-outputphase measurement.
 21. The circuit of claim 20, wherein the test signalgenerator is adapted to couple a test signal into the input of thenonlinear circuitry and sweep a frequency and an amplitude of the testsignal.
 22. The circuit of claim 21, wherein the test signal comprisestwo tones of different frequencies, and the frequency for sweeping isthe difference between the different frequencies of the two tones. 23.The circuit of claim 22, wherein the test signal has exactly two tonesof different frequencies.
 24. The circuit of claim 20, wherein themeasurement unit is further configured to record a set of measurementresult vectors, wherein complex value elements of each measurementresult vector represent magnitude and phase of the output signal fordifferent input signal amplitudes at a given input signal frequency. 25.The circuit of claim 24, wherein the calculation unit is adapted tocalculate the transfer functions of the filters on the basis of the setof measurement result vectors.
 26. A circuit for determining aconfiguration of a predistorter to linearize a nonlinear circuitryhaving an input and an output, the predistorter comprising one or morestatic nonlinear elements and a plurality of linear filters withtransfer functions, comprising: a test signal generator coupled to theinput of the nonlinear circuitry; a measurement unit coupled to theoutput of the nonlinear circuitry and configured to perform an inputamplitude-to-output amplitude measurement and an inputamplitude-to-output phase measurement of the nonlinear circuitry; and acalculation unit operably coupled to the measurement unit and adapted tocalculate the transfer functions on the basis of results of the inputamplitude-to-output amplitude measurement and input amplitude-to-outputphase measurement.
 27. The circuit of claim 26, wherein the test signalgenerator is adapted to couple a test signal into the input of thenonlinear circuitry and sweep a frequency and an amplitude of the testsignal.
 28. The circuit of claim 27, wherein the test signal comprisestwo tones of different frequencies, and the frequency for sweeping isthe difference between the different frequencies of the two tones. 29.The circuit of claim 28, wherein the test signal has exactly two tonesof different frequencies.
 30. The circuit of claim 26, wherein themeasurement unit is further configured to record a set of measurementresult vectors, wherein complex value elements of each measurementresult vector represent the magnitude and phase of the output signal fordifferent input signal amplitudes at a given input signal frequency. 31.The circuit of claim 30, wherein the calculation unit is adapted tocalculate the transfer functions of the filters on the basis of the setof measurement result vectors.
 32. The circuit of claim 31, wherein thecalculation unit is adapted to calculate transfer functions from thefrequency responses of the filters.
 33. The circuit of claim 26, whereinthe predistorter comprises a baseband predistorter, and wherein thestatic nonlinear elements and linear filters thereof are configured torepresent memory polynomials.